Algebrized approach for the finite element analysis of heterogeneous viscoelastic structures

The analysis of heterogeneous structures in the linear viscoelastic field is a common problem for reinforced concrete and prestressed concrete structures. The analysis is complicated by the form of the constitutive law that includes a Volterra integral, whose analytical evaluation is possible only for simple models and simple histories of the prescribed variables. For general applications, proper numerical methods are thus needed which require the use of specific software usually available in research environments only. This paper suggests an approach that makes use of the method originally proposed by Trost and actually referred to as Age Adjusted Effective Modulus (AAEM) to overcome the difficulties related to the integration over time. It is shown that the proposed method can be easily coupled with standard linear elastic finite element strategies in order to convert them to the analysis of viscoelastic structures as well. Some illustrative examples prove the simplicity of this approach and the good level of accuracy achieved.